{"id":"https://openalex.org/W7214711103","doi":"https://doi.org/10.48550/arxiv.2609.33350","title":"KoopCell: Koopman-Based Generative Model for Learning Single-Cell Dynamics from Distribution Snapshots","display_name":"KoopCell: Koopman-Based Generative Model for Learning Single-Cell Dynamics from Distribution Snapshots","publication_year":2026,"publication_date":"2026-09-27","ids":{"openalex":"https://openalex.org/W7214711103","doi":"https://doi.org/10.48550/arxiv.2609.33350"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33350","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33350","pdf_url":"https://arxiv.org/pdf/2609.33350","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.33350","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136754448","display_name":"Wanfeng Lu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu, Wanfeng","raw_affiliation_strings":["Research Institute of Intelligent Complex Systems , Fudan University , China","School of Mathematical Sciences , SCMS, SCAM, and CCSB , Fudan University , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute of Intelligent Complex Systems , Fudan University , China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"School of Mathematical Sciences , SCMS, SCAM, and CCSB , Fudan University , China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153480255","display_name":"Yutong Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Yutong","raw_affiliation_strings":["Institutes of Brain Science , Fudan University , China","Research Institute of Intelligent Complex Systems , Fudan University , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institutes of Brain Science , Fudan University , China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Research Institute of Intelligent Complex Systems , Fudan University , China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138051027","display_name":"Keyi Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou, Keyi","raw_affiliation_strings":["Research Institute of Intelligent Complex Systems , Fudan University , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute of Intelligent Complex Systems , Fudan University , China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032111699","display_name":"Chenxin Ge","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ge, Chenxin","raw_affiliation_strings":["Research Institute of Intelligent Complex Systems , Fudan University , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute of Intelligent Complex Systems , Fudan University , China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153535865","display_name":"Wei Lin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001690369","display_name":"Qunxi Zhu","orcid":"https://orcid.org/0000-0001-7281-5274","observed_orcids":["https://orcid.org/0000-0001-7281-5274"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Qunxi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.5044000148773193,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.5044000148773193,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.33329999446868896,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.1216999962925911,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/koopman-operator","display_name":"Koopman operator","score":0.9079999923706055},{"id":"https://openalex.org/keywords/single-cell-dynamics","display_name":"single-cell dynamics","score":0.7020000219345093},{"id":"https://openalex.org/keywords/population-dynamics","display_name":"population dynamics","score":0.6050000190734863},{"id":"https://openalex.org/keywords/non-markovian-effects","display_name":"non-Markovian effects","score":0.8629999756813049},{"id":"https://openalex.org/keywords/single-cell-rna-sequencing","display_name":"single-cell RNA sequencing","score":0.8140000104904175}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5878000259399414},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.541700005531311},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5087000131607056},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5001999735832214},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4814000129699707},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.47380000352859497},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4668000042438507},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.46219998598098755},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4205000102519989},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.3772999942302704},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3646000027656555},{"id":"https://openalex.org/C40506919","wikidata":"https://www.wikidata.org/wiki/Q7452469","display_name":"Sequence learning","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.34439998865127563},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3287000060081482},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30489999055862427},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2953999936580658},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.295199990272522},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.295199990272522},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.26919999718666077},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.259799987077713},{"id":"https://openalex.org/C177255742","wikidata":"https://www.wikidata.org/wiki/Q4109953","display_name":"Branching process","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2563000023365021}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33350","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33350","pdf_url":"https://arxiv.org/pdf/2609.33350","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.33350","doi":"https://doi.org/10.48550/arxiv.2609.33350","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33350","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.33350","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33350","pdf_url":"https://arxiv.org/pdf/2609.33350","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214711103.pdf","grobid_xml":"https://content.openalex.org/works/W7214711103.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1641836978","https://openalex.org/W2058825331","https://openalex.org/W2078898317","https://openalex.org/W2110065044","https://openalex.org/W2127141656","https://openalex.org/W2131866773","https://openalex.org/W2166574880","https://openalex.org/W2418021230","https://openalex.org/W2594932112","https://openalex.org/W2772716190","https://openalex.org/W2800912249","https://openalex.org/W2900069807","https://openalex.org/W2969535312","https://openalex.org/W3002219094","https://openalex.org/W3008658832","https://openalex.org/W3017511136","https://openalex.org/W4280596398","https://openalex.org/W4300374450","https://openalex.org/W4399608272","https://openalex.org/W4402253248","https://openalex.org/W4404342654","https://openalex.org/W4407377247","https://openalex.org/W4417298435"],"related_works":["https://openalex.org/W7131616665","https://openalex.org/W7214700442","https://openalex.org/W7221785833","https://openalex.org/W2999580658","https://openalex.org/W4417454630","https://openalex.org/W7116688893","https://openalex.org/W4391940570","https://openalex.org/W4415016618","https://openalex.org/W4417116585","https://openalex.org/W4412454272"],"abstract_inverted_index":{"Learning":[0],"population":[1,30],"dynamics":[2,113],"from":[3,87],"temporally":[4],"sparse,":[5],"unpaired":[6],"distribution":[7,88],"snapshots":[8,89],"is":[9],"a":[10,54,79,115],"fundamental":[11],"challenge":[12],"in":[13],"developmental":[14,49],"biology.":[15],"Recent":[16],"approaches":[17],"based":[18,58],"on":[19,59,119],"neural":[20],"differential":[21],"equations":[22],"and":[23,41,66,90,122,140],"flow":[24],"matching":[25],"can":[26],"interpolate":[27],"between":[28],"observed":[29],"snapshots,":[31],"but":[32],"may":[33],"struggle":[34],"to":[35,132,142],"extrapolate":[36],"beyond":[37],"the":[38,73,84,110,127,152],"training":[39],"horizon":[40],"often":[42],"lack":[43],"an":[44],"explicit":[45],"mechanism":[46],"for":[47,83],"modeling":[48],"branching.":[50],"We":[51],"propose":[52],"KoopCell,":[53],"unified":[55],"generative":[56],"framework":[57,131],"Koopman-Mori-Zwanzig":[60],"theory":[61],"that":[62],"jointly":[63],"learns":[64],"representations":[65],"predictive":[67],"linear":[68],"latent":[69,111],"dynamics.":[70],"Theoretically,":[71],"using":[72],"weak":[74],"continuity":[75],"equation,":[76],"we":[77,101],"derive":[78],"closed-form":[80],"least-squares":[81],"estimator":[82],"Koopman":[85,112,134],"generator":[86],"establish":[91],"convergence":[92],"guarantees":[93],"under":[94],"suitable":[95],"assumptions.":[96],"To":[97],"model":[98,136],"branching":[99,137],"dynamics,":[100],"further":[102],"develop":[103],"KoopCell-M,":[104],"which":[105],"incorporates":[106],"non-Markovian":[107],"memory":[108],"into":[109],"through":[114,138],"Markovian":[116],"embedding.":[117],"Experiments":[118],"synthetic":[120],"systems":[121],"three":[123],"scRNA-seq":[124],"datasets":[125],"demonstrate":[126],"ability":[128],"of":[129],"our":[130],"recover":[133],"spectra,":[135],"memory,":[139],"scale":[141],"predicting":[143],"high-dimensional":[144],"gene":[145],"expression":[146],"distributions,":[147],"achieving":[148],"state-of-the-art":[149],"performance":[150],"among":[151],"evaluated":[153],"methods.":[154]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}